Even if you have the right of way you can still be found partially at fault if an accident results from your failure to use reasonable care to avoid the collision.

In Cox v. Weil, the plaintiff sought to recover for injuries stemming from a three car pile up at an intersection that was controlled by a traffic light. Weil moved for summary judgment arguing that the green light was in his favor and the co-defendant ran the red light. Weil admitted, however, that he did not see the other vehicle prior to impact.

In denying the motion for summary judgment, the court held that drivers are entitled to a reasonable expectation that other drivers will obey the traffic laws and yield the right of way, but a driver who lawfully enters an intersection after the light turns green must still exercise reasonable care to avoid the accident.

http://www.courts.state.ny.us/reporter/3dseries/2009/2009_07222.htm